Disclaimer: I don't know your knees, what is wrong with them, etc. Anything I say here could make matters worse. I do not know what loose knees are. Do you hyperextend your knees?

To build strength:
Wall sits with a block between your knees - the block helps you align your legs, and for many people takes the pain out of the knee. You could do the same thing in Utkasana (chair pose)
Warrior 1 & 2 - you could either build up time with your knee less than 90 degrees or you could place a block at the wall on your shin (toes up the wall or not, depending of the length of your foot)
Anytime you are have straight legs, lift your quadriceps (engage the muscles of your thighs)

Hope that helps

I've had a lot of knee issues myself (torn ACLs and torn meniscus for a total of 5 knee surgeries), but there are so many possibilities with knees it is a bit hard to know what to recommend.

I will say that chair pose with careful attention to form has been very helpful. Warrior poses are helpful for me too, but again with very careful alignment. Don't go any deeper than feels good and makes sure your knees are stacked over your ankles. And if Warrior 1 is putting any stress on your back knee with the twisting, it's better to modify it to a high lunge where you are up on your toes, and maybe bend your knee a tiny bit (especially if you are prone to hyperextension).

And tone/activate the muscles in your entire legs when you can and that will help build strength. Whether you're standing in mountain pose or in down dog or whatever. The tip about lifting your kneecaps is great, and you can also think about your adductors (inner thighs) and hamstrings and everything all active at once to keep the knee joint balanced and straight. You can hang out in those poses or work your legs in those poses, so focus on making those muscles you want to build all activate and do their job.

I enjoy Anusara style yoga in particular for that as the focus on inner spiraling the legs really makes my leg muscles work and the teacher I go to focuses on that a lot. Like in down dog with one leg lifted - that lifted leg he wants with all the muscles toned and working hard. It's a good reminder for me.

I'm also not sure if this applies to you, but I've found in the past that sometimes I was afraid to "try too hard" for fear of being too worn out for the rest of the class. Kind of in energy conservation mode (haha, maybe ego conservation mode). It's helped me to drop that mental attitude and if I wear myself out and need to sit in childs pose for part of class, so be it! That's not to say push through joint pain obviously - because that's an entirely different thing, but push through the muscles shaking and fear of being too worn out to continue. I thought about it one day and realized I'm not out on a hike in the middle of nowhere where I need to conserve energy for the trip back home - I can just sit down if my muscles are ever truly "done". So don't be afraid to make your muscles work, because pushing them a reasonable amount is where that muscle growth comes from.

On the bright side - my knees aren't structurally stable like they used to be (I'm missing a lot of meniscus, etc.) - but the strength I've gotten from yoga and biking make them feel strong and stable overall. So stick with it with both activities!

Good point - tree pose/warrior 3/etc. Those balance poses are good ones too for helping create stability in your knees.

There's another one that my teacher calls "arrow lunge" though it's a little different than what google comes up with for the most part...

It's basically this: http://farm1.staticflickr.com/188/457354385_079b7db57e.jpg

But then you work on straightening your back leg so you are balancing on the top of your back foot and the knee/shin are lifted off the ground. You can/should start with your hands on the ground or on blocks, then maybe put your hands on your front knee, then move to the full pose. Warning though that for me, this one felt utterly impossible on my knees at first, but it's a great quad strengthener. At first I wasn't really lifting at all, just flexing the muscles and moving towards almost lifting my knee/shin off the ground. Now it's not that big of a deal, but like everything, go into it very slow and see what it feels like for your knees.